scholarly journals Stress channelling in extreme couple-stress materials Part I: Strong ellipticity, wave propagation, ellipticity, and discontinuity relations

2016 ◽  
Vol 88 ◽  
pp. 150-168 ◽  
Author(s):  
Panos A. Gourgiotis ◽  
Davide Bigoni
Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Yanqi Wu ◽  
Jianwei Ma

In elastostatics, the scale effect is a phenomenon in which the elastic parameters of a medium vary with specimen size when the specimen is sufficiently small. Linear elasticity cannot explain the scale effect because it assumes that the medium is a continuum and does not consider microscopic rotational interactions within the medium. In elastodynamics, wave propagation equations are usually based on linear elasticity. Thus, nonlinear elasticity must be introduced to study the scale effect on wave propagation. In this work, we introduce one of the generalized continuum theories—couple stress theory—into solid earth geophysics to build a more practical model of underground medium. The first-order velocity-stress wave equation is derived to simulate the propagation of Rayleigh waves. Body and Rayleigh waves are compared using elastic theory and couple stress theory in homogeneous half- space and layered space. The results show that couple stress causes the dispersion of surface waves and shear waves even in homogeneous half-space. The effect is enhanced by increasing the source frequency and characteristic length, despite its insufficiently clear physical meaning. Rayleigh waves are more sensitive to couple stress effect than body waves. Based on the phase-shifting method, it was determined that Rayleigh waves exhibit different dispersion characteristics in couple stress theory than in conventional elastic theory. For the fundamental mode, the dispersion curves tend to move to a lower frequency with an increase in characteristic length l. For the higher modes, the dispersion curves energy is stronger with a greater characteristic length l.


1993 ◽  
Vol 60 (4) ◽  
pp. 857-865 ◽  
Author(s):  
K. Mrithyumjaya Rao ◽  
M. Pratap Reddy

A detailed study of a Rayleigh wave propagating on the surface of a micropolar elastic circular cylinder in an azimuthal direction is considered. At the cutoff frequency if the particle displacement is purely azimuthal and equivoluminal, then only this type of wave exists. A number of deviations from the results of the classical theory are observed. For example, the phase velocity corresponding to the same branch is given to be single valued, whereas it seems to be multivalued at some intervals. Due to the micropolar effect there exists an extra wave whose frequency spectrum is also obtained. The dependence of the microrotation and couple stress amplitudes on depth are evaluated. The frequency of the Rayleigh wave increases due to the micropolar effect.


1974 ◽  
Vol 64 (2) ◽  
pp. 387-392
Author(s):  
M. Farshad ◽  
G. Ahmadi

abstract The surface-wave propagation in a half-space according to couple-stress theory is studied herein. Dispersion curves as well as displacement variations with the depth coordinate are obtained for a range of material parameters. Comparison is made with the classical elasticity predictions upon which certain conclusions are reached.


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